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[t] A textured image sieved to five scales using a <math>\mathcal{M}</math>-sieve. Resulting Channel images are Bi-polar. Red is used to denote +ve granules and blue -ve granules. fe

Our algorithm uses sieve operators to sieve each texture image to scales, <math>\left[s_{1}\ldots s_{N}\right]</math> where <math>\log_{10} s_{n}</math> are equispaced between 0 and <math>\log_{10}S_{max}</math>, <math>S_{max}</math> is the maximum chosen scale and <math>N</math> the number of sieved images. Tex-Mex features are formed from statistics derived from channel images. Noting that the setting <math>S_{max} = 30</math> removes all the texture from the images and setting <math>N = 5</math> results in five images sieved to scales <math>\left[1,2,5,13,30\right]</math>. Five channel images are formed from these sieved images at scales 0 to 1, 1 to 2, 2 to 5, 5 to 13 and 13 to 30. Figure [fe] shows some example sieved images and resulting channel images. The intensity of the granule, or channel, images as a function of scale is an indicator of the scale-distribution of the texture features.


For image retrieval, stereo-matching and object recognition the current interest is in finding regions in the image that are likely to remain unaffected by noise, projective transformations, compression and lighting change. In a comprehensive set of trials  a type of region known as Maximally Stable Extremal Regions (MSERs) were found to be the best performing. It turns out that MSERs are generated by a variant of the sieve algorithm known as open/close-sieves. It is therefore possible to parse a sieve tree and to generate

Stable Salient Contours

(SSCs) which are carefully selected nodes from the sieve tree that have all the stability and robustness properties associated with MSERs. Thus, as in Figure [fig:treesal] the sieve tree generates stable regions “for free�.

Colour sieves

The sieve has recently been extended into the color domain  via the use convex hulls to define color extrema which are then merged to their nearest neighbours, found using a Euclidean distance measure. Figure [colPepdecomp] shows an example color sieve decomposition of a sample image.


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